Nanotube junctions

ABSTRACT

The present invention comprises a new nanoscale metal-semiconductor, semiconductor-semiconductor, or metal-metal junction, designed by introducing topological or chemical defects in the atomic structure of the nanotube. Nanotubes comprising adjacent sections having differing electrical properties are described. These nanotubes can be constructed from combinations of carbon, boron, nitrogen and other elements. The nanotube can be designed having different indices on either side of a junction point in a continuous tube so that the electrical properties on either side of the junction vary in a useful fashion. For example, the inventive nanotube may be electrically conducting on one side of a junction and semiconducting on the other side. An example of a semiconductor-metal junction is a Schottky barrier. Alternatively, the nanotube may exhibit different semiconductor properties on either side of the junction. Nanotubes containing heterojunctions, Schottky barriers, and metal-metal junctions are useful for microcircuitry.

[0001] This invention is disclosed in provisional application serial No.60/011065 and this application claims benefit of the provisional filingdate, Feb. 2, 1996.

[0002] This invention was made with U.S. Government support underContract No. DE-AC03-76SF00098 between the U.S. Department of Energy andthe University of California for the operation of Lawrence BerkeleyLaboratory. The U.S. Government may have certain rights in thisinvention.

I. BACKGROUND OF THE INVENTION

[0003] 1. Field of the Invention

[0004] This invention relates generally to microelectronics and morespecifically to metal-semiconductor, metal-metal, andsemiconductor-semiconductor junctions in nanotubes.

[0005] 2. Description of Related Art

[0006] The electronic structure of carbon nanotubes is governed in partby the geometrical structure of the tube (R. Saito et al., Appl PhysLett, 60:2204, 1992; and N. Hamada et al., Phys Rev Lett. 68:1579,1992).

[0007] A nanotube index (n,m) has been developed to describe thenanotube structure. It is described in detail by C. T. White et al.“Predicting Properties of Fullerenes and their Derivatives”, Chapter 6,page 159 and following, in Buckminsterfullerenes, W. E. Billups, and M.A. Ciufolini, ed. (NY: VCH Publishers, 1993). Carbon nanotubes can beunderstood by thinking of them as a graphite sheet, in which the carbonatoms are arranged in a honeycomb lattice of hexagonal rings. The sheetis rolled up and spliced together to form a tube. That is, the tube is aconformal mapping of the two dimensional sheet onto the surface of acylinder. The two-dimensional lattice sheet can be rolled many differentways to form a tube. The nanotube index describes how a sheet is rolledinto the tube. A special circumference vector is related to the numberof adjacent hexagonal carbon rings that are traversed when tracing thetube circumference once, and the amount the lattice is skewed when it isrolled. The lattice vector, R, is made up of two component vectors, R,and R₂, where R=nR₁+mR₂ with n and m integers or zero.

[0008] Electrical properties of nanotubes are associated with thenanotube index as follows:

[0009] 1. Carbon nanotubes having a nanotube index in which n=m, forexample, (5,5) or (9,9), are metals. These nanotubes conduct electricalcurrent.

[0010] 2. Carbon nanotubes, characterized by an index of (n,m) where n−mis a nonzero multiple of three, for example, (6,3) or (12,0). Thesenanotubes have a band-gap that is typically less than 0.1 eV,characteristic of semiconductors or semimetals. The size of the band-gapis inversely proportional to the tube radii. However, if the radius isvery small as described by X. Blase et al., Phys Rev. Lett. 72: 1878,1994, in which case, the large curvature further modifies the nanotubeelectrical properties.

[0011] 3. Carbon nanotubes having nanotube indices different from thosedescribed above, for example, (7,0) or (13,4), are semiconductors thathave a band-gap size up to approximately 1 eV. The size of the band-gapis inversely proportional to the tube radius (J. W. Mintmire et al.,Mater. Res. Soc. Sym. Proc. 247:339, 1992).

[0012] Typically, a useful junction of two semiconductors requires thatthe two semiconductors have band-gaps whose difference exceeds theelectron thermal energy.

[0013] T. W. Ebbesen and T. Takada (Carbon, 33: 973, 1995) have notedthat the index of a tube can be changed by introducing topologicaldefects into the hexagonal bond network of carbon. Theoreticallynanotubes can be constructed to have a particular index and exhibitparticular electrical properties. To result in a useful structure, thedefects may not induce a net curvature which might cause the tube eitherto flare or to close, and minimal local curvature surrounding theinduced defect is desirable to minimize any defect energy. Since defectscan change the index in a nanotube, they are considered to be the causeof some flaring or closing of the tube structure as a result of theintroduced defect in the hexagonal carbon lattice.

[0014] While some researchers have described nanotubes having any of asingle pair of indices, (n,m), no-one has described how a continuoustube could be formed having separate sections that would becharacterized by different indices, (n₁, m₁) and (n₂, m₂).

[0015] No-one has discovered a means to change the nanotube index withina continuous carbon nanotube without causing the net curvature to changeso that one end closes or flares. Another way to say this is that no onehas found a way to join two carbon nanotubes having different nanotubeindices to form a continuous tube.

[0016] It would be highly desirable and useful to alter the index withina continuous tube in a manner that that does not change the netcurvature of the tube but does alter the nanotube's electricalproperties on either side of specific point so that adjoining sectionsof the nanotube are semiconducting, non-conducting, or conducting asneeded for semiconductor devices and circuits. Another way of statingthis is that it would be very useful to be able to join two nanotubeshaving different indices through a junction.

II. SUMMARY OF THE INVENTION

[0017] It is an object of the invention to design carbon nanotubescontaining adjacent sections of differing electrical properties. Thesenanotubes can be constructed from combinations of carbon, boron,nitrogen and other elements. It is a further object of the invention todesign carbon nanotubes in which the nanotube index is different oneither side of a junction point in the tube so that the electricalproperties on either side of the junction vary in a useful fashion. Forexample, a carbon nanotube may be electrically conducting on one side ofa junction and semiconducting on the other side. An example of asemiconductor-metal junction is a Schottky barrier. Alternatively, thecarbon nanotube may exhibit different semiconductor properties on eitherside of the junction. A junction that joins materials having differentsemiconducting properties on either side of the junction is sometimesreferred to as a heterojunction. Nanotubes containing heterojunctions,Schottky barriers, and metal-metal junctions are useful formicrocircuitry.

[0018] The present invention comprises a new nanoscalemetal-semiconductor, semiconductor-semiconductor, or metal-metaljunction, made by introducing topological defects in the essentiallyhexagonal carbon atom structure of a carbon nanotube. The defects changethe carbon lattice arrangement such that the nanotube index on one sideof the defect is characteristic of metal properties and the index on theother side of the defect is characteristic of semiconductor properties.A junction is thus formed at the site of the defect. The inventivenanotube comprises carbon bonded in an essentially hexagonal array,wherein the array contains some non-hexagonal carbon rings. Thenon-hexagonal rings comprise a defect that changes the index and forms ajunction point in the nanotube. The point where the index changes, thatis the point where the defect exists, forms a junction between carbonnanotubes having different electrical conduction properties. Theinvention comprises essentially carbon nanotubes havingmetal-semiconductor junctions, semiconductor-semiconductor junctions,and metal-metal junctions. Similar junction effects can be achieved innanotubes with local chemical additions, subtractions, or substitutions.

III. SUMMARY DESCRIPTION OF THE DRAWINGS

[0019]FIG. 1: schematically shows the atomic structure of a carbonnanotube in which a heptagon-pentagon carbon-ring structure has beenintroduced.

[0020]FIG. 2: shows a transmission electron micrograph of a carbonnanotube with an extended pentagon-heptagon defect.

[0021]FIG. 3: shows the Density of States (DOS) verses Energy for thesemiconducting section of a nanotube having nanotube index (8,0), andadjoining a (7,1) section.

[0022]FIG. 4: shows the Density of States verses Energy for theconducting, metallic, section of a nanotube having nanotube index (7,1),and adjoining a (8,0) section.

[0023]FIG. 5: shows the Density of States verses Energy for thesemiconducting section of a nanotube having nanotube index (8,0), andadjoining a (5,3) section.

[0024]FIG. 6: shows the Density of States verses Energy for thesemiconducting section of a nanotube having nanotube index (5,3), andadjoining a (8,0) section.

[0025]FIG. 7a: shows a side view of the structure of a carbon nanotubehaving two electrically conducting sections on either side of a junctionin the carbon lattice, wherein the electron resonances in each sectionare different.

[0026]FIG. 7b: shows a view down the long axis of the same tube, lookingtoward the junction.

[0027]FIG. 8: shows a nanotube having oppositely-orientedpentagon-heptagon pairs.

IV. DETAILED DESCRIPTION OF THE INVENTION

[0028] The inventive carbon nanotube comprises a junction that forms aboundary between two essentially carbon sections having differentelectrical properties. The two sections on either side of the junctionare characterized by different nanotube indices. The difference inelectrical properties of the carbon nanotube sections relates to thesize of the band-gap. The band-gap in one section may be so small thatthe tube in that section is electrically conducting and has metalliccharacteristics, while the size of the band-gap in the other section ischaracteristic of a semiconductor. Alternatively, the junction mayseparate two different semiconductor forms of the carbon nanotube, ortwo different metallic forms of a carbon nanotube.

[0029] Use of the term “band-gap” herein means the energy separating thevalence band from the conduction band in a material.

[0030] Use of the term “defect” herein means a ring of carbon atomsbonded together, within an essentially carbon lattice, in which thereare either more than six or less than six carbon atoms.

[0031] Use of the term “hexagon” herein means a six-membered ring ofcarbon atoms.

[0032] Use of the term “pentagon” herein means five-membered ring ofcarbon atoms.

[0033] Use of the term “heptagon” herein means seven-membered ring ofcarbon atoms.

[0034] Use of the term “pentagon-heptagon pair” herein means oneseven-membered carbon ring and one five-membered carbon ring.

[0035] Use of the term “adjacent pentagon-heptagon pair” herein meansone seven-membered carbon ring and one five-membered carbon ring whereintwo atoms are members of both a five-membered carbon ring and aseven-membered carbon ring.

[0036] Use of the term “extended pentagon-heptagon pair” herein meansone seven-membered carbon ring and one five-membered carbon ring whereinno atoms are members of both rings.

[0037] Each section of the nanotube is comprised essentially of carbonbonded in an essentially hexagonal lattice. The geometrical arrangementof the lattice, for example the extent to which adjacent hexagons in thelattice form a helix on the surface of the tube, is designated by ananotube index (n,m). The geometry of the defect free nanotube, asdescribed by the nanotube index, determines the electrical properties ofthe nanotube. For example, carbon nanotubes having a nanotube index inwhich n=m, for example, (5,5) or (9,9), are metals. Carbon nanotubescharacterized by an index of (n,m) where n−m is a nonzero multiple ofthree, for example, (6,3) or (12,0), have band-gap less than 0.1 eV andare characteristic of semiconductors or semimetals. Carbon nanotubeshaving nanotube indices different from those described above, forexample, (7,0) or (13,4), are semiconductors having band-gaps up to 1.0eV and decreasing in proportion to the nanotube radius.

[0038] Wherever non-hexagonal carbon rings are introduced into theessentially hexagonal lattice, the nanotube index changes. Thenon-hexagonal ring is referred to as a “defect” because it forms anirregularity in the essentially hexagonal structure of the carbonlattice. A defect that changes the nanotube index, and concomitantly theelectrical properties, without causing the tube to flare or to close,forms a junction. It is termed a junction because the electricalproperties are dissimilar on either side of the junction. In addition toforming a metal-semiconductor junction in the carbon nanotube, asemiconductor-semiconductor or metal-metal junction can be formed.

[0039] The junction in the inventive nanotube comprises rings that forma pentagon and a heptagon in the otherwise essentially hexagonal carbonlattice. In other words, two carbon nanotubes having different indices,can for the first time, be joined using a nanotube section containing atleast one pentagonal and at least one heptagonal carbon ring. There mustbe one pentagonal carbon ring for each heptagonal ring in the junction.There may be many more than one pentagon-heptagon pair in the junctiondepending on the size and nanotube index of the nanotube sections to bejoined at the junction. The inventive junction comprises the carbonnanotube section that contains the pentagon and hexagon “defect” in theessentially hexagonal lattice.

[0040] Varying the position of the carbon pentagon ring with respect tothe carbon heptagon ring within the junction varies the nanotube indexon either side of the junction. When the pentagon and heptagon areadjacent, but not aligned either with the long axis of the tube or withthe circumference of the tube, a nanotube having indices of (n,m) on oneside of the junction joins to a nanotube having indices of either(n+1,m−1) or (n−1,m+1) on the other side of the junction. In anotherexample, if the pentagon and heptagon are adjacent and are aligned withthe long axis of the tube, a nanotube having a indices of (n,0) on oneside of the junction joins, through thepentagon-heptagon-pair-containing junction, to a tube having a nanotubeindex of either (n+1,0) or (n−1,0).

[0041] The inventive junction may comprise a pentagon ring that is notadjacent to the heptagon ring. In this case the nanotube section on oneside of the junction has a radius that is different from the radius onthe other side of the junction. The difference in radii of the twosections is proportional to the distance between the pentagon ring andthe heptagon ring.

[0042] A constant diameter tube geometry is retained on both sides ofthe junction only when the junction comprises at least one pentagoncarbon ring and one heptagon carbon ring. The pentagon and heptagon maybe adjacent or separated by several hexagons. The pentagon and heptagonmay lie in a line parallel to the long axis of the tube, or they may liein a line that forms an angle with the long axis of the tube. There maybe more than one pentagon and one heptagon in the junction. The moststable relative position of a heptagon and pentagon pair is when theyare adjacent. A junction comprising a single heptagon defect in theessentially hexagon lattice causes the tube on one side of the junctionto taper and close. A junction comprising a single pentagon defect inthe essentially hexagon lattice causes the tube to flare and expand.

[0043] A junction comprising one or more pentagon-heptagon pairs in agiven configuration joins two semi-infinite semiconducting nanotubesections having different band gaps. This means that overall, thejunction neither causes one section of the tube to flare nor to close.Alternatively the junction may be configured to join an electricallyconducting section to a semiconducting section. It is further possibleto design a junction that joins two conducting nanotube sections.

[0044] The inventive semiconductor-semiconductor junction carbonnanotube in which nanotube sections having band-gaps that differ by morethan the thermal energy of a free electron are joined together, can bedoped with to become a p-n junction.

[0045] A low dimension quantum well device can be constructed by joiningtwo large band-gap semiconducting carbon nanotubes to either end of asmall band-gap semiconducting nanotube. The difference in band-gap sizesis greater than the thermal energy of a free electron. The resultingnanotube comprises three sections having a small band-gap sectionsurrounded by two large band-gap sections. The small band-gap sectionacts like a quantum well, and has useful properties in optics andelectronics. The inventive carbon semiconductor-semiconductor junctionnanotubes are also useful design nanocircuits having a variety ofband-gap sizes positioned at specific locations with respect toone-another.

[0046]FIG. 1 schematically illustrates an inventive carbon nanotube 2.Each circle, or ball, in the structure represents a carbon atom 4. Thelines between the carbon atoms represent carbon-carbon bonds 6. It canbe seen that the carbon atoms are essentially arranged in hexagonalrings 8. Two rings in the illustrated nanotube are not hexagonal andthey are highlighted, by use of open circles. One forms a pentagon 10and the other forms an adjacent heptagon 12. This inventive nanotube wascreated by introducing a pentagon-heptagon carbon ring-pair into thehexagonal carbon ring structure. The pentagon-heptagon ring-pair wasdiscovered to be the smallest topological defect that could beintroduced into the hexagonal structure while maintaining minimal localcurvature and no net curvature. At the same time, the introduction ofthis pentagon-heptagon ring-pair causes the helicity and the nanotubeindex, and thus the electrical properties, of the carbon nanotube tochange.

[0047] The lower portion of the nanotube 14 shown in FIG. 1 has ananotube index of (8,0). Since 8-0 is not an integral multiple of 3, noris n=m, this portion of the tube is a semiconductor having a band-gap ofup to 1 eV. The upper section of the illustrated nanotube 16 has ananotube index of (7,1). In this case 7−1=6, which is an integralmultiple of 3, and section 16 of the nanotube has metallic conductivity(i.e. the band gap is so small it behaves as a metal). The junctioncomprises a pentagon-heptagon pair 10, and 12, at the junction point.Thus, the nanotube illustrated in FIG. 1 is a nanoscale electronicelement that can be used to make devices like Schottky barriers, quantumwells, and transistors.

[0048] For semiconductor nanotubes, wherein the nanotube index is not(n,n) and n−m is not equal to 3 times an integer, the band-gap isinversely proportional to the diameter of the nanotube. The diameter ofthe nanotube is limited on the small side by the bond energy of thecarbon lattice. As the nanotube diameter decreases, the degree ofcurvature in the nanotube wall increases and the carbon bond energybegins to influence the band-gap. The lattice energy limits theusefulness of the nanotube as a semiconductor when the nanotube diameteris less than or equal to about 0.5 nm. It is an important factor whenthe diameter is between about 0.5 nm and about 0.7 nm. For nanotubediameters between about 0.7 nm and about 1.0 nm, the lattice energyresulting from curvature modifies the inverse relationship betweennanotube diameter and semiconductor band-gap size, but not significantlyenough to limit the utility of nanotubes having diameters in that sizerange.

[0049] For semiconductor nanotubes, wherein the nanotube index is not(n,n) and n−m is not equal to 3 times an integer, the usefulness of thenanotube is limited on the large side by the decreasing band-gap size.At room temperature, a nanotube having a 40 nm diameter has a band-gapof about 0.02 eV. Since room temperature electrons have an energy of0.02 eV, they jump easily from the valence band to the conduction bandand the nanotube does not act as a semiconductor at room temperature. Atlower temperatures, where the electron thermal energy is less, ananotube of 40 nm diameter may satisfactorily behave as a semiconductor.

[0050] It can be seen that there are at least three ways to design anelectrically conducting, metallic, carbon nanotube section: 1) designthe tube diameter large enough that the band-gap decreases to theelectron thermal energy; 2) design the tube such that it has a nanotubeindex where n=m; or 3) design the tube to have indices where n−m=3 timesan integer and wherein the band-gap is smaller than the thermal energyof a free electron.

[0051] The number of pentagon-heptagon pairs used in the junction andtheir alignment with the axis of the nanotube, determines the nanotubeindex and the diameter of the nanotube section on either side of thejunction. These parameters, in turn, determine the semiconductorproperties each section of the nanotube has.

[0052] In general carbon-nanotubes having indices in which neither n norm are zero can be connected to tubes having indices of either (n−1,m+1)or (n+1,m−1) through a junction having a single adjacentpentagon-heptagon pair. A junction having two pentagon-heptagon pairsoriented in the same direction joins a carbon nanotube section havingnon-zero indices, (n,m), to a carbon nanotube section having (n−2,m+2)or (n+2,m−2). The pattern continues for 3 or more pentagon-heptagoncarbon-ring pairs. If p is the number of axially alignedpentagon-heptagon pairs in the junction, it connects a carbon nanotubesection (n,m) on one side to a carbon nanotube (n−p, m+p) or (n+p,m−p)on the other side. It will be clear to one of ordinary skill in the artthat junctions containing different numbers of pentagon-heptagon pairsconnect metal-like and semiconductor-like carbon nanotubes in manydifferent permutations.

[0053] An arrangement of two pentagon-heptagon pairs oriented inopposite directions does not change the indices of the tube (i.e. (n,m)goes to (n+1−1,m+1−1)=(n,m)). However, this arrangement changes thelocal electrical properties of the tube. The region of the tube within 1nanometer of any pentagon or heptagon comprising the twooppositely-oriented pentagon-heptagon pairs has increased metalliccharacter. The effect of introducing an oppositely-oriented pair ofpentagon-heptagon defects in a semiconductor tube is to reduce its bandgap. The effect of introducing an oppositely-oriented pair ofpentagon-heptagon defects in a metallic tube is generally to increasethe density of states.

[0054] A carbon nanotube having one index equal to zero, (n,0), isjoined to a (n+1,0) or to a (n−1,0) through a junction having oneadjacent pentagon-heptagon pair aligned parallel to the axis of the(n,0) tube. If the heptagon is on the side of the (n,0) section, itjoins that section to a (n+1,0) nanotube; if the pentagon is on the sideof the (n,0) section, it joins that section to a (n−1,0) nanotube.

[0055] It is not necessary for the pentagon and heptagon to be adjacentin the junction; instead an extended pentagon-heptagon pair can be usedin the junction. When the pentagon and heptagon are separated byessentially hexagonal carbon rings, the nanotube index of the nanotubesections joined on either side of the inventive junction can vary by anyamount depending on the number of intervening hexagons. For example, ifonly one hexagon separates the pentagon and the heptagon, then thejunction connects an (n,0) nanotube with a (n+2,0) or an (n−2,0)nanotube. The general rule is, a nanotube having a (n,0) index is joinedto a nanotube having a (n+p+1,0) or (n−p−1,0) where p is the number ofhexagons intervening between the pentagon and the heptagon. When theheptagon is oriented to the (n,0) side, the joined tube has nanotubeindex (n+p+1,0); when the pentagon is oriented to the (n,0) side, thejoined tube has nanotube index (n−p−1,0).

[0056] An extended pentagon-heptagon pair is also used to form ajunction that joins a carbon nanotube having an index (n,m) whereneither n or m is zero, to a carbon nanotube having an index of either(n+1+p,m−1+p) or (n−1+p,m+1+p) or (n+1−p,m−1−p) or (n−1−p,m+1−p). Thesign of the number, ±1, is determined by the angle the extendedpentagon-heptagon pair makes with respect to the (n,m) tube axis. Thesign of the term, ±p, is determined by the orientation of the extendedpentagon-heptagon pair with respect to the (n,m) side. The greater theextension of the junction, i.e. the greater the distance betweennon-adjacent pentagon-heptagon pairs, the greater the difference is inthe diameters of the joined tubes. However, because the bond energyincreases proportionally to the distance between non-adjacentpentagon-heptagon pairs, nanotubes having junctions containing extendedpentagon-heptagon pairs are less stable than junctions made withadjacent pentagon-heptagon pairs.

[0057] One configuration of the inventive junction results in a junctionbetween two electrically conducting carbon nanotubes wherein currentdoes not transfer across the junction. This occurs when the wavefunctionfor the electrons have different symmetries on either side of thejunction. This condition is obtained when the pentagon-heptagon pairs inthe junction are arranged in a symmetrical geometry.

[0058] The inventive carbon nanotubes can be doped with other atoms, forexample boron (B) or nitrogen (N), to add p or n type carriers. Thecarriers are attracted to the parts of the device having the smallerband gaps. Doping further enhances the utility and flexibility of theinventive nanotubes. This geometry allows the fabrication of rectifyingor gated electronic and optical devices.

[0059] A junction marks a transition in electrical properties along theaxis of a tube. It is possible to design junctions that match tubeshaving different electrical properties without using pentagon-heptagonpairs. For example, junctions can be designed in which the transition inelectrical properties occurs due to differences in chemical composition.Yet another way to join nanotubes having different electrical propertiesis to join tubes having a different concentration of oppositely-orientedpentagon-heptagon pairs on either side of the joining point, or junctionpoint.

[0060] For example, a carbon tube with indices (n,m) can be joined to aboron nitride tube with indices (n,m) without introduction of anytopological defects. The band-gap on the boron nitride side of thejunction is between about 4 and about 5 volts. Since the carbon tube canbe either metallic or semiconducting, a junction formed by substitutingboron nitride for some of the carbon atoms, creates either ametal-semiconducting junction or a semiconducting-semiconductingjunction. Any ratio of boron, carbon, and nitrogen may be used (e.g.,B_(x)C_(y)N_(z)). The process of making these chemical substitutions isdescribed in Phys. Rev. B Vol. 51 page 11229 (1995).

[0061] Changes in chemical composition can also be created byintroducing dopant atoms that are in contact with either the inside orthe outside of the nanotube walls. These atoms change the electricalproperties of the former essentially carbon nanotube, by transferringelectrons to or from the tube. For example, alkali atoms such aspotassium or rubidium donate electrons to the tube when they are incontact with the nanotube walls. Variations in the concentration of suchatoms along the axis of a tube creates a transition in electricalproperties.

EXAMPLE 1

[0062] TEM of Junction Nanotube

[0063]FIG. 2 shows a transmission electron microscope photograph of theinventive carbon nanotube having an extended pentagon-heptagon pair inthe junction The interior wall of the tube 20 is darkened forphotographic clarity. The positions of a heptagon 22 and pentagon 24were inferred by performing geometrical constructions and noting thelocations at which tubes with parallel walls join the junction 26. Thiscarbon nanotube was synthesized, isolated, and imaged via transmissionelectron microscopy using conventional experimental methods [S. Iijima,Nature 354, pgs. 56-58, (1991)].

[0064] Tubes can also be created which have more than one concentricwall. These tubes are known as multiwalled tubes. FIG. 2 shows amultiwalled tube. The parallel strips above the interior wall 20 arecross-sectional cuts of many concentric tubes. Multiwalled tubes can bedesigned with junctions as described above existing in the individualwalls, yielding structures with transitions in overall electricalproperties. These junctions can be between two metals, a metal and asemiconductor, or between two semiconductors of different band gaps.

EXAMPLE 2

[0065] Semiconductor/Metal Junction

[0066]FIG. 1 shows an (8,0) carbon nanotube joined to a (7,1) carbonnanotube The circled atoms 10 and 12 comprise the adjacentpentagon-heptagon pair that forms the junction. The structure can bedenoted as (8,0)/(7,1) in analogy with interfaces of bulk materials. Bycalculating the electronic structure using quantum theory we find thatfar from the interface the (7,1) section is a semimetal and the (8,0)section is a semiconductor having a moderate band-gap. The two sectionsand the junction combine to form a quasi one-dimensionalsemiconductor/metal junction, taking into account that the band-gap issmall enough in the (7,1) nanotube section that it approximately behaveslike a metal. The inventive structure, unlike other semiconductor/metaljunctions, is essentially composed of a single chemical element.

[0067] A tight quantum-based tight-binding model having one π-orbitalper atom along with the Surface Green Function Matching method (SGFM)(F. Garcia-Moliner and V. R. Velasco, Theory of Single and MultipleInterfaces, World Scientific, Singapore, 1992) was used to calculate thelocal density of states (LDOS) in different regions of two archetypalsections (n,m₁/n₂,m₂) joined through an appropriate junction. Inparticular, a (8,0)/(7,1) semiconductor/semi-metal carbon nanotube wasexamined The unit cells of the perfect nanotubes were matched at theinterface without the addition of extra atoms by using a singlepentagon-heptagon pair.

[0068] Using the tight-binding m-electron approximation [X. Blase etal., Phys. Rev. Lett. 72:1878 (1994)], the (8,0) section has a 1.2 eVgap and the (7,1) section is a semimetal. Within the tight bindingapproximations, these tubes form an archetypal semiconductor/metaljunction. We found that curvature-induced σ-π hybridization modifiedthese band-gaps. In particular, within the local density approximation(LDA) the gap of the (8,0) section was 0.62 eV and the (7,1) section hada band-gap less than 0.1 eV. Qualitatively the (7,1) section behavedlike a metal, when the π-electron tight binding treatment was used, soit was possible to examine this tube as a semiconductor/metal junction.

[0069] The local density of states in various regions on both sides ofthe (8,0)/(7,1) junction. The π-electron tight-binding Hamiltonian is ofthe form,$H = {{{- V_{{pp}\quad \pi}}{\sum\limits_{i\quad j}{a_{i}^{\dagger}a_{j}}}} + {c.\quad c.}}$

[0070] where i and j are restricted to nearest neighbors; andV_(ppπ)=2.66 eV [using the π-π nearest neighbor hopping parameter of X.Blase et al.] The on-site energy is set equal to zero. Within thistheory, graphite sheets and defect-free nanotube have completeelectron-hole symmetry with their Fermi levels at zero. For simplicityall nearest-neighbor hoppings were assumed to be equal, independent ofthe length, location and orientation of the bonds on the matched tubes.Deviations in bond lengths due to reconstruction near the interface wereneglected. Hence, the changes in local electronic structure were studiedsolely as a result of changes in the connectivity on the lattice.

[0071] To determine the LDOS of two joined semi-infinite nanotubes, theGreen function was calculated using the SGFM method. Details concerningthis formalism can be found in the Garcia-Moliner reference above. TheSGFM technique allowed the Green function of a composite system, formedby joining two semi-infinite media, to be calculated, using the Greenfunctions of the two infinite constituent systems. Thus, knowing theGreen functions of the defect-free (n₁,m₁) and (n₂,m₂) nanotubes, theGreen function of the nanotube system formed by joining twosemi-infinite tubes, (n₁,m₁/n₂,m₂) can be constructed. Knowledge of theGreen function allows the local density of states (LDOS) to be extractedat any site on the combined structure. For sections, three regions weredefined each successively more distant from the junction. The LDOS ofcomparably situated region was compared for several nanotube structures.

[0072] The results for the (8,0)/(7,1) nanotube structure was plotted asshown in FIGS. 3 and 4. The first three panels of FIG. 3 show regionsdefined by a unit-cell. The LDOS were averaged for each of three regionsin the (8,0) section of the nanotube. The last panel shows the densityof states (DOS) of a defect-free (8,0) nanotube. The regions arenumbered beginning from the junction, so region 1 of the (8,0) sectionis in contact with the junction and region 1 of the (7,1) section. TheLDOS was averaged over each region because quantum interference effectsdistort the LDOS on individual atomic sites. The region in the (8,0)nanotube section comprises a circumferential ring of hexagons having 32atoms. A unit cell in the (7,1) section has 76 atoms, so instead ofdefining a region as a unit cell in this section, FIG. 4 shows regionsin the (7,1) section as carbon rings containing 32-atoms. In this waythe local density of states on either side of the junction can bedirectly compared as a function of distance from the junction.

[0073]FIG. 3 shows that the LDOS on the (8,0) semiconducting section ismost distorted in region 1, the region nearest the junction. Acoincidental alignment of the bands farthest from the Fermi level in theasymptotic regions on either side of the junction suggests that thedifference from the defect-free DOS is biggest for energies near the gapfor this specific junction. In particular, region 1 shows allowed statesin the energy range of the gap of the infinite (8,0) section. Thesemetal-induced gap states (V. Heine, Phys Rev. 138:1689 (1965); S. G.Louie and M. L. Cohen, Phys. Rev. B 13:2461 (1976)] are characteristicof a metal-semiconductor junction. These states disappear rapidly withdistance from the junction, as shown in the plots for regions 2 and 3 inFIG. 3. As distance from the junction increases, the defect-freenanotube DOS features appear: in region 3, all the van Hovesingularities of the infinite nanotube can be clearly identified.

[0074]FIG. 4 shows the LDOS for the (7,1) section averaged over regionscontaining 32-atoms. This is somewhat fewer atoms than are contained ina unit cell, but the 32 atom range was used so results could be comparedto those of the (8,0) section.

[0075] The band-gap in the (7,1) carbon nanotube section was so smallthat it essentially behaved like a metal, that is like a conductor. TheLDOS around the Fermi energy (0 eV) in the metallic (7,1) nanotubesection was essentially unchanged. The van Hove singularities present inthe last panel showing the LDOS for a defect-free (7,1) section are, inthe first panel showing region 1, smeared out, with the exception ofthose at the highest and lowest energies. With increasing distance fromthe junction, features characteristic of the infinite (7,1) nanotubeappear in the (7,1) section of the (8,0)/(7,1) carbon nanotube. In panel3 of FIG. 4, showing the LDOS for region 3 of the (7,1) section, all thefeatures of the defect-free (7,1) nanotube are identifiable.

EXAMPLE 3

[0076] Semiconductor/Semiconductor Junction

[0077] A (8,0)/(5,3) semiconductor/semiconductor carbon nanotube wasexamined using the same techniques as above. The heterojunction joiningthe unit cells of the (8,0) and (5,3) nanotube sections was formed usingthree pentagon-heptagon pairs and two hexagons. Two different junctionconfigurations were possible: one having the two hexagons adjacent andone having the hexagons separated. The sequence of n-membered carbonrings encountered when tracing around the circumference of the nanotubeheterojunction was: 6, 7, 5, 6, 7, 5, 7, 5.

[0078] The band-gap of a defect-free (5,3) nanotube is 1.4 eV 0.2 eVlarger than that of the (8,0) nanotube. The (8,0)/(5,3) nanotube thusprovides a prototypical example of a semiconductor/semiconductorheterojunction.

[0079] The methods used to determine the LDOS was the same as describedin Example 2.

[0080] The results for the (8,0)/(5,3) semiconductor-semiconductorheterojunction are plotted in FIGS. 5 and 6. For the same reasons ofcomparison as above, the LDOS for the (5,3) nanotube section wasaveraged over closed regional containing 32 atoms instead of unit cells.Two defect states appear in the gap near the junction. The geometricdistortions due to the three pentagon-heptagon pairs in the junctionregion create states in the gap in a manner similar to that seen in bulksemiconductor interfaces. The bond distances in the junction were notchanged, so the appearance of these new states are attributed to thechanges in the lattice connectivity, that is, to the alteration of thenetwork topology. These interface states may pin the Fermi energy of thesemiconductor-semiconductor tube.

[0081] The interface states have maximal LDOS in region 1 of the (8,0)Their amplitudes are appreciable in 5 consecutive 32-atom rings,circumference regions, a 12Å distance along the nanotube axis. Theamplitudes decay faster with distance from the junction in the (5,3)section. This behavior is expected because (5,3) is the large band-gapsemiconductor section. As was observed in the previous example, the LDOSin the junction region is the most distorted; features of the perfect(5,3) and (8,0) nanotubes appear some distance away from the junctionregion. The prominence of the interface states in this junction was aconsequence of the presence of three pentagon-heptagon pairs. Other,junctions, that match semiconductor sections with similar band-gapoffsets, can be obtained with only a single pentagon-heptagon pair and aconsequently reduced density of interface states. In this example, aconfiguration was chosen to minimize the difficulty of the calculations.

EXAMPLE 4

[0082] Gated Conductive Channel

[0083] A nanocircuit electrical switch is formed by joining two metalliccarbon-nanotube-sections to either end of a semiconductorcarbon-nanotube-section. This nanotube does not conduct a current fromend to end. However, applying sufficient negative voltage to thesemiconducting section enables the three-section nanotube to conductcurrent from end to end. In light of the teaching above, one of ordinaryskill in the art can configure such a device.

EXAMPLE 5

[0084] Conductor-Conductor Junction

[0085] A junction was designed that connects two carbon nanotubesections wherein each section is electrically conducting, but in whichcurrent is not conducted across the junction.

[0086] An integral number of electron wavefunction oscillations must fitaround the circumference of a nanotube. One could make an analogy to theintegral number of oscillations that appear on a vibrating string. Thenumber of oscillations defines the angular symmetry of the electronicwavefunctions. In designing this tube, it is useful to concentrate onthe highest energy electrons (those near the Fermi energy) since theseare the electrons which determine the electrical properties of thenanotube.

[0087] A special form of junction was designed by joining two metallicnanotubes in which the highest energy electronic states in each tube haddifferent angular symmetries. Because the atomic arrangement at theinterface between the nanotubes has a compatible symmetry, the highestenergy electrons from one side of the nanotube do not propagate into theother tube. In this situation the metal-metal junction does not conduct.

[0088] The angular symmetries of the electronic states are determinedfollowing the method of N. Hamada et al Physical Review Letters Vol. 68page 1579 (1992). The angular symmetry of the interface is compatiblewith zero conduction if the angular symmetry of the interface is also aangular symmetry of the nanotubes on either side.

[0089] In summary, a junction between two metallic nanotubes wasdesigned in which the electrons do not conduct a current across thejunction because of different symmetries in the electronic states oneither side of the junction. A similar situation (in which theelectronic states on either side of a junction have different angularsymmetries) has been designed for junctions between two semiconductorsor a semiconductor and a metal.

[0090] An external perturbation that breaks this symmetry conditionallows a current to flow across the junction. The amount of current isproportional to the strength of the perturbation. Examples of suchperturbations are external stress, illumination by light, or the randomatomic motions associated with finite temperature. Because the device isvery sensitive to external perturbations which weaken the symmetrycondition, the device is useful as a detector of these perturbations.

[0091] This inventive nanotube design is shown in FIG. 7A. Section 28 iselectrically conducting wherein the conducting electron has a specificelectron resonance, or waveform. Section 32 is electrically conductingwherein the conducting electron has a specific electron resonance, orwaveform that is different from that of section 28.

[0092] The two conducting sections are joined to a junction 30 thatcomprises three pentagon-heptagon pairs. Atoms belonging tothe,pentagon-heptagon pairs are shown as dark, filled circles in thelattice. Each pentagon-heptagon pair has the orientation of the pentagonand heptagon in the same direction, approximately pointing around thecircumference of the tube, and each pentagon-heptagon pair is separatedby an intervening hexagon. Rings 34, 36, 38, and 40 show respectively, aheptagon ring, a pentagon ring, a hexagon ring (arrows point to the sixatoms of the hexagon ring), and a heptagon ring. The next pentagon isnot visible because it is wrapping around the underside of the tube.

[0093]FIG. 7B shows a view of the junction from inside the nanotube,looking down its axis. The junction comprising three pentagon-heptagonpairs oriented to approximately encircle the circumference of the tubecan clearly be seen. Each pentagon-heptagon pair, 34′ and 36′, 40′ and42, 46 and 48, is separated from the next pentagon-heptagon pair by ahexagon, 38′, 44, 50. Two atoms of each intervening hexagon ring arealso members of a heptagon ring in one pentagon-heptagon pair, while twoatoms on the opposite side of the intervening hexagon are also membersof a pentagon in a different pentagon-heptagon pair. In this figure,rings 34′, 36′, 38′, 40′ correspond to similarly numbered rings in FIG.7A. Section 28 is in the foreground of FIG. 7B and section 32 ispictured beyond the junction.

EXAMPLE 6

[0094] A carbon nanotube is designed that incorporates a concentrationof oppositely-oriented pentagon-heptagon pairs in its lattice network.If the tube is a semiconductor, the band-gap decreases with increasingconcentration of pentagon-heptagon pairs. If the tube is a metal ornear-metal, the LDOS increases with increasing concentration ofpentagon-heptagon pairs. That is, the metallic character of the tube isenhanced as the concentration of pentagon-heptagon pairs increases.

[0095]FIG. 8 illustrates a tube having oppositely-orientedpentagon-heptagon pairs. Atoms that are members of a pentagon-heptagonpair are represented as dark, filled circles in the carbon lattice. Thenumber referring to a ring is located in the center of the ring. Rings52 and 54 form a pentagon-heptagon pair as do rings 56 and 58.Oppositely-aligned pentagon-heptagon pairs are located in regions alongthe tube to change the local properties of the tube, for example to makea conducting “pad” or region on the tube. Alternatively, theconcentration of pentagon-heptagon pairs within a tube section could beapproximately uniformly distributed in the tube section to increase theglobal conductivity of that section.

[0096] Two tubes having different concentrations of pentagon-heptagonpairs can be designed to join into a continuous nanotube havingdifferent electrical properties on either side of the joining point. Inthis case the junction is at the interface between the two tubes ratherthan a comprising a pentagon-heptagon pair. Instead, thepentagon-heptagon pairs form part of the structure of at least one ofthe nanotube sections.

[0097] Nanotube junctions comprising pentagon-heptagon pairs provide awide range of device possibilities for doped and undoped nanotubes madeof carbon and/or other elements. By arranging the pentagon-heptagonpairs at various points along the length of a carbon nanotube, a seriesof junctions can be introduced that influence the electronic structureof the tube on either side of each junction. A variety of carbon-basedquasi-one-dimensional quantum wells and superlattices with band offsetsof about 0.1 eV can be configured using the inventive junctions. Inaddition, a gated conducting channel can be configured using a suitablevoltage source. The Fermi level of a metallic pure carbon nanotube lieswithin the band-gap of a similar semiconductor nanotube. As such, eithern-type or p-type doping of the semiconductor section of ametal/semiconductor interface yields a device similar to a Schottkybarrier.

[0098] The experimental signature of a pentagon-heptagon pair junctionis an abrupt bend between two straight section of nanotube. A tightbinding molecular dynamics scheme [C. H. Xu et al. J. Physics-CondensedMatter, 4:6047(1992)] was used on a finite system to calculate the bendangles. For a junction with a single pentagon-heptagon pair, angles ofbetween about 10° and about 15° were obtained. The exact value dependedon the particular characteristics of the tubes either side of thejunction. An approximately 14° bend was observed in a multiwalled purecarbon nanotube [N. Koprinarov, et al. J. Phys. Chem. 99:2042(1995)].

[0099] Thus, the invention provides a new type of metal/semiconductor,semiconductor/semiconductor or metal/metal junction, made essentially ofa single element, and based solely on the introduction of one or morepentagon-heptagon pairs in, for example, the essentially hexagonalgraphite lattice of carbon nanotubes. Two archetypical junctions havebeen extensively modeled and one has been fabricated and verifiedthrough TEM. These junction provide the elements to manufacturenanoscale semiconductor devices.

[0100] The description of illustrative embodiments and best modes of thepresent invention is not intended to limit the scope of the invention.Various modifications, alternative constructions and equivalents may beemployed without departing from the true spirit and scope of theappended claims.

Having thus described the invention, what is claimed is:
 1. A nanotubejunction comprising at least one five-membered carbon ring and at leastone seven-membered carbon ring in an essentially six-membered carbonring lattice.
 2. A carbon nanotube junction comprising at least onepentagon-heptagon pair.
 3. The carbon nanotube junction of claim 2wherein the pentagon-heptagon pairs are adjacent pentagon-heptagonpairs.
 4. The carbon nanotube junction of claim 2 wherein thepentagon-heptagon pairs are extended pentagon-heptagon pairs.
 5. Acontinuous essentially carbon nanotube comprising, a) a firstelectrically conducting section of nanotube; b) a second semiconductingsection of nanotube joined to the first section.
 6. The nanotube ofclaim 5 further comprising a junction having at least onepentagon-heptagon pair, adjoined on one side to the electricallyconducting section and on the other side to the semiconductor section.7. The nanotube of claim 5 wherein the semiconducting section comprisescarbon pentagon-heptagon pairs distributed approximately uniformlythroughout its length.
 8. The nanotube of claim 5 wherein theelectrically conducting section comprises carbon pentagon-heptagon pairsdistributed approximately uniformly throughout its length.
 9. Thenanotube of claim 5 wherein the semiconducting section and theelectrically-conducting section comprise carbon pentagon-heptagon pairsdistributed approximately uniformly throughout their lengths, theconducting section having a higher concentration of pentagon-heptagonpairs than the semiconducting section.
 10. The nanotube of claim 5wherein the semiconducting section comprises electron-donating dopantatoms.
 11. The nanotube of claim 5 wherein the electrically-conductingsection comprises electron-donating dopant atoms.
 12. The nanotube ofclaim 5 wherein both the semiconducting section and theelectrically-conducting section comprise electron-donating dopant atoms.13. The nanotube of claim 5 wherein the semiconducting section compriseselectron-accepting dopant atoms.
 14. The nanotube of claim 5 wherein theelectrically-conducting section comprises electron-accepting dopantatoms.
 15. The nanotube of claim 5 wherein both the semiconductingsection and the electrically-conducting section compriseelectron-accepting dopant atoms.
 16. A continuous essentially carbonnanotube comprising, a) a first semiconducting section; b) a secondsemiconducting section joined to the first section; wherein the band-gapof the first section differs from the band-gap of the second section bymore than the thermal energy of a free electron.
 17. The nanotube ofclaim 16 further comprising a junction having at least onepentagon-heptagon pair, adjoined on one side to the semiconductornanotube having a smaller band-gap and on the other side to thesemiconductor nanotube having a larger band-gap.
 18. The nanotube ofclaim 16 wherein one of the semiconducting sections comprises carbonpentagon-heptagon pairs distributed approximately uniformly throughoutits length.
 19. The nanotube of claim 16 wherein both of thesemiconducting sections comprise carbon pentagon-heptagon pairsdistributed approximately uniformly throughout their lengths, one of thesections having a higher concentration of pentagon-heptagon pairs thanthe other section.
 20. The nanotube of claim 16 wherein one of thesemiconducting sections comprises electron-donating dopant atoms. 21.The nanotube of claim 16 wherein both of the semiconducting sectionscomprise electron-donating dopant atoms.
 22. The nanotube of claim 16wherein one of the semiconducting sections comprises electron-acceptingdopant atoms.
 23. The nanotube of claim 16 wherein both of thesemiconducting sections comprise electron-accepting dopant atoms.
 24. Acontinuous essentially carbon nanotube comprising, a) a firstelectrically-conducting section; b) a second electrically-conductingsection joined to the first section; in which the highest energyelectronic states in each section have different angular symmetries. 25.The nanotube of claim 24 further comprising a junction having at leastone pentagon-heptagon pair, adjoined on one side to one of theelectrically-conducting sections and on the other side to the other ofthe electrically-conducting sections.
 26. The nanotube of claim 24wherein one of the electrically-conducting sections comprises carbonpentagon-heptagon pairs distributed approximately uniformly throughoutits length.
 27. The nanotube of claim 24 wherein both of theelectrically-conducting sections comprise carbon pentagon-heptagon pairsdistributed approximately uniformly throughout their lengths.
 28. Thenanotube of claim 24 wherein one of the electrically-conducting sectionscomprises electron-donating dopant atoms.
 29. The nanotube of claim 24wherein both of the electrically-conducting sections compriseelectron-donating dopant atoms.
 30. The nanotube of claim 24 wherein oneof the electrically-conducting sections comprises electron-acceptingdopant atoms.
 31. The nanotube of claim 24 wherein both of theelectrically-conducting sections comprise electron-accepting dopantatoms.
 32. A continuous essentially carbon nanotube comprising, a) afirst semiconducting section having a nanotube index of (8,0); b) asecond semiconducting section having a nanotube index of (5,3) joined tothe first section; c) a junction comprising three pentagon-heptagonpairs and two six-membered carbon rings.
 33. A continuous essentiallycarbon nanotube comprising, a) a first electrically conducting sectionof nanotube having a nanotube index of (7,1); b) a second semiconductingsection of nanotube having a nanotube index of (8,0), joined to thefirst section; and c) a junction one pentagon-heptagon pair.
 34. Acontinuous essentially carbon nanotube comprising, a) a firstelectrically-conducting section; b) a second electrically-conductingsection joined to the first section; and c) a junction comprising threepentagon-heptagon pairs and three six-membered carbon rings.
 35. Acontinuous essentially carbon nanotube having a p-n junction comprising,a) a nanotube section having a nanotube index characteristic of n-typesemiconductors; b) a nanotube section having a nanotube indexcharacteristic of p-type semiconductors; and c) a junction comprising atleast one pentagon-heptagon pair, adjoined on one side to the n-typesection and on the other side to the p-type section.
 36. A continuousessentially carbon nanotube having gated conduction propertiescomprising, a) a first nanotube section having electrical propertiescharacteristic of metals; b) a second nanotube section having electricalproperties characteristic of semiconductors, joined to the firstsection; c) a third nanotube section having electrical propertiescharacteristic of metals, joined to the second section; and d) aconducting region in the second section through which a voltage can beapplied to the second section.
 37. A continuous essentially carbonnanotube having properties of a quantum well comprising, a) a firstnanotube section having electrical properties characteristic of metals;b) a second nanotube section having electrical properties characteristicof semiconductors, joined to the first section; and c) a third nanotubesection having electrical properties characteristic of metals, joined tothe second section.
 38. A continuous nanotube comprising, a) anessentially carbon nanotube section, and b) a carbon nanotube section inwhich atomic substitutions are made, chosen from the group comprisingboron and nitrogen.
 39. The nanotube of claim 38 wherein p-type orn-type dopants are added.